Volume of Pyramids, Cones, and Spheres
Ever wonder how much space is inside a pyramid or a ball? Let's break down these volume formulas so you can solve problems easily!
For a rectangular pyramid, the volume equals one-third of the base area times the height: V = ⅓Bh (where B = L×W). If you have a triangular pyramid, the formula is similar, but the base area is calculated differently: V = ⅓Bh (where B = ½b₁b₂).
Cones follow a similar pattern to pyramids. Their volume is one-third of the base area times the height: V = ⅓πr²h. For spheres, the formula is V = ⅘πr³, where r is the radius of the sphere.
💡 Quick Tip: All these formulas include a fraction (⅓ or ⅘) multiplied by the base area or the cube of the radius. Remember that the base area changes depending on the shape!
Let's look at an example: For a triangular pyramid with a base of 9ft by 12ft and height of 10ft, we calculate: V = ⅓(½×9×12)×10 = ⅓(54)×10 = 180ft³
When solving these problems, take it one step at a time - first find the base area, then multiply by height, and finally multiply by the fraction in the formula.